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Flexible bioelectronics, guided by mechanics and computation, can better fit to a curving body.

Flip phones are everywhere these days. Engineers from the University of Wisconsin-Madison and the University of Texas at Austin used a model that predicts how well flexible electronics will fit on spherical surfaces, ushering in a new era of seamless integration of these flexible devices with parts of the human bodyle devices with parts of the human body. body. In the future, for example, flexible bioelectronic artificial retinas implanted in human eyes could help restore vision, or smart contact lenses could continuously measure glucose levels in the body.

“With a robust simulation model, we can immediately predict compliance, which can greatly speed up the flexible electronics design process,” said Ying Li, associate professor of mechanical engineering at UW-Madison, where the research team developed the computer model. “Simulation results provide very clear guidelines for the experimenter, who can determine the optimal design without conducting time-consuming experiments.”

The researchers detailed their work in an article published in the journal Science Advances on April 19, 2023.

“With our powerful simulation model, we can now predict conformability instantly, which dramatically speeds up the design process for flexible electronics.” The simulation results provide very clear direction for experimentalists, who can now decide the ideal design without having to conduct a large number of exceedingly time-consuming tests.”

Ying Li, an associate professor of mechanical engineering at UW–Madison.

To function as intended, bioelectronic devices must be in very close contact with living tissue and must not bend or wrinkle. However, researchers have had difficulty fully adapting flexible electronics to the “hard surfaces” found throughout the human body—ball-shaped surfaces that cannot be flattened without breaking or bending.

In this study, the research team used a combination of experimental, analytical, and numerical approaches to systematically investigate how partially cut circular sheets as well as circular polymer sheets (which mimic the mechanical properties of flexible electronic devices) conform to spherical surfaces. By analyzing these results, the researchers were able to derive ready-to-use formulas that reveal the underlying physics and predict the deformation of flexible electronic devices.

“The results from our three different methods revealed the same interesting physics,” said Nanshu Lu, a professor in the Department of Aerospace Engineering and Technological Mechanics at the University of Texas at Austin, who led the experimental study. “We have formulated very simple mathematical equations to guide the design of flexible electronics for maximum fit, which will have significant implications in the field.”

The researchers also demonstrated a simple and elegant method that greatly improves the flexible sheet’s ability to conform to spherical surfaces. Inspired by the Japanese art of paper cutting and folding, the researchers made the simplest radial incisions in circular sheets, improving formability by 40% to 90%. Lee said these advances will spur innovation in the field, allowing many more researchers to design more advanced flexible electronic devices.

“This is the first paper to provide a complete picture of the complex process of how flexible electronics adapt to such complex surfaces,” says Lee. “These advances pave the way for all future research to develop bioelectronics that are more adaptable to the human body.”

More information: Siyi Liu et al, Conformability of flexible sheets on spherical surfaces, Science Advances (2023). DOI: 10.1126/

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